**Constitutive equations** describe the behavior of a material subjected to certain loading conditions.

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**Constitutive equations in elastostatics:**

In case of a geometric linear perspective the constitutive law is a function of an infinitesimal distortion

\mathbf{\epsilon} = \frac{1}{2} \left(\frac{\partial\mathbf{u}}{\partial\mathbf{x}} + \left(\frac{\partial\mathbf{u}}{\partial\mathbf{x}}\right)^T\right)

In linear elasticity theory, we have the generalized Hooke’s law

\mathbf{\sigma} = \mathbb{C}[\epsilon]

where \mathbb{C} defines the positive definite stiffness tensor of the material.

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